Prospective in (Primate) Dental Analysis through Tooth 3D ... · functional importance of...
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Prospective in (Primate) Dental Analysis through Tooth3D Topographical QuantificationFranck Guy*, Florent Gouvard, Renaud Boistel, Adelaıde Euriat, Vincent Lazzari
Centre National de la Recherche Scientifique, Institut Ecologie et Environnement, UMR 7262 – iPHEP: Institut de Paleoprimatologie et Paleontologie Humaine, Evolution et
Paleoenvironnements, Universite de Poitiers, Faculte des Sciences, Poitiers, France
Abstract
The occlusal morphology of the teeth is mostly determined by the enamel-dentine junction morphology; the enamel-dentine junction plays the role of a primer and conditions the formation of the occlusal enamel reliefs. However, theaccretion of the enamel cap yields thickness variations that alter the morphology and the topography of the enamel–dentine junction (i.e., the differential deposition of enamel by the ameloblasts create an external surface that does notnecessarily perfectly parallel the enamel–dentine junction). This self-reliant influence of the enamel on tooth morphology ispoorly understood and still under-investigated. Studies considering the relationship between enamel and dentinemorphologies are rare, and none of them tackled this relationship in a quantitative way. Major limitations arose from: (1) thedifficulties to characterize the tooth morphology in its comprehensive tridimensional aspect and (2) practical issues inrelating enamel and enamel–dentine junction quantitative traits. We present new aspects of form representation basedexclusively on 3D analytical tools and procedures. Our method is applied to a set of 21 unworn upper second molarsbelonging to eight extant anthropoid genera. Using geometrical analysis of polygonal meshes representatives of the toothform, we propose a 3D dataset that constitutes a detailed characterization of the enamel and of the enamel–dentinejunction morphologies. Also, for the first time, to our knowledge, we intend to establish a quantitative method forcomparing enamel and enamel–dentine junction surfaces descriptors (elevation, inclination, orientation, etc.). New indicesthat allow characterizing the occlusal morphology are proposed and discussed. In this note, we present technical aspects ofour method with the example of anthropoid molars. First results show notable individual variations and taxonomicheterogeneities for the selected topographic parameters and for the pattern and strength of association between enamel–dentine junction and enamel, the enamel cap altering in different ways the ‘‘transcription’’ of the enamel–dentine junctionmorphology.
Citation: Guy F, Gouvard F, Boistel R, Euriat A, Lazzari V (2013) Prospective in (Primate) Dental Analysis through Tooth 3D Topographical Quantification. PLoSONE 8(6): e66142. doi:10.1371/journal.pone.0066142
Editor: Luca Bondioli, Museo Nazionale Preistorico Etnografico ‘L. Pigorini’, Italy
Received February 11, 2013; Accepted May 1, 2013; Published June 24, 2013
Copyright: � 2013 Guy et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricteduse, distribution, and reproduction in any medium, provided the original author and source are credited.
Funding: This work was made possible by the Centre of Microtomographie of the University of Poitiers and supported by the Agence Nationale de la Recherche(ANR-09-BLAN-0238) and the region Poitou-Charentes (Conventions Region #07/RPC-R-100 & #12/RPC-013). The funders had no role in study design, datacollection and analysis, decision to publish, or preparation of the manuscript.
Competing Interests: The authors have declared that no competing interests exist.
* E-mail: [email protected]
Introduction
Tooth is a central element in many fields of investigation
especially in anthropology and paleoanthropology as a key tissue
for taxonomic identification, phylogenetic or biological inferences
(e.g. [1–16]). In this regard, many aspects of the teeth size and
shape have been considered by researchers over the last century,
from detailed description of the occlusal morphology to the
characterization of the underlying developmental processes of the
tooth form (e.g. [5,17]) including quantification of various
dimensional aspects of the teeth by a wide variety of descriptors
(e.g. [3,12,18–26]).
The recent technological advances in capturing objects’
tridimensional morphology by mean of noninvasive methods
(e.g. CT and mCT-scans, laser-scanning, …) and the improvement
of image analysis tools allowed renewing tooth studies (see e.g.
[10,12,15,17,18,20–21,24,26–28]). Not only researchers are able
to consider an extensive set of dental features in their analyses
including crown enamel and enamel-dentine junction, roots and
pulp canals (see e.g. [29–32]), but also they are able to consider
these tissues in their comprehensive tridimensional aspects.
Thus, 3D image analytical tools offer the opportunity to
appraise and characterize both morphology and properties of the
dental tissues in a quantitative way. On one side geometric
morphometric-based methods consist in describing shape by the
use of landmarks, semi-landmarks and outline coordinates. These
powerful methods allow independently analyzing size and shape
and have been successfully applied to tooth shape studies (e.g.
[9,19,33–34]). Such methods describe effectively occlusal outline
of the teeth as well as occlusal cusp pattern, i.e. the way the cusp
are positioned relatively to each other. On the other side
biomechanics like finite element analysis try to explain the
functional importance of morphological traits, apart from a metric
quantification of the morphological features (e.g. [35]). Between
these two poles of the tooth analysis, numerous methods can be
found taking into account both morphology and function. Hence,
relationships between dental morphology and function may be
approached using quantitative descriptors of the tooth surface like
microwear analyses and tooth tribology for assessing diet, or
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Occlusal Fingerprint Analysis for evaluating cusp interlocking
pattern and occlusal tooth wear (e.g. [3,36–41]). Besides, tooth
form and function can be accessed through topographical analysis
of the occlusal surface using GIS software (e.g. [15,36,42]). Also,
other methods like surface deviation analysis or virtual cartogra-
phy and morphometric map procedures are routinely applied in
medical and anthropological sciences although mostly focusing on
thickness measurement of cortical bone and tooth enamel
[24,28,43–46]. Rigorously, assessing dental evolution requires
taking into account all the results issued from the above mentioned
methods as they provide complementary evidences. In this paper
we will focus on data retrievable from topographical analyses. We
present an original approach combining 3D topographical analysis
of the occlusal enamel surface (OES) and the occlusal enamel-
dentine junction surface (EDJ), and their geometrical relationship
using surface deviation analysis-based method. We aim to propose
a comprehensive characterization of the tooth occlusal morphol-
ogy using 3D positioning and distribution of topographical
(elevation, inclination, orientation) and material (enamel thickness)
descriptors of the dental features.
While the use of topographical and surface deviation analysis
procedures has been proved to be of significant interest in
paleontological and paleoanthropological studies, notably for
qualitative and quantitative characterization of the dental form
[36,47–51], their potential are still underexploited. Classically,
GIS studies recurrently invoke, at various steps, data reduction
procedures from 3D to 2D. While such a loss of information in a
2D approach may be rewarded by a better readability of the
results and a stronger statistical power, GIS studies tend to
dispose of potentially crucial information or to mask numerous
features (e.g. re-entrant angles and vertical surfaces linked to
particular enamel morphologies, regions under bent cusp tips,
protuberances, walls of grooves, regions close to the cervix, or
below the maximum crown diameter, are not considered (e.g.
[36,47–48]). We present here new aspects of tooth form
representation based exclusively on 3D image analytical tools
and procedures which allow avoiding such limitations, topo-
graphical variables being implemented in a fully tridimensional
context.
Moreover, studies considering the relationship between enamel
and dentine morphologies are rare, and none of them tackled this
relationship in a quantitative way. Yet, the tooth morphology, i.e.,
the occlusal morphology of the crown enamel develops from the
enamel-dentine junction (EDJ, [5,17,52–53]). The EDJ plays the
role of a primer and conditions the formation of the occlusal
enamel reliefs. Nevertheless, the way the EDJ acts on enamel
morphology albeit of primary interest in dental studies, remains
insufficiently characterized and not quantified. For the first time,
to our knowledge, it is possible to comprehensively quantify OES
(outer enamel surface) and EDJ (enamel-dentine junction)
topographical covariations.
We applied our procedure to a set of anthropoid, unworn to
slightly worn, left upper second molars. The resulting 3D dataset
constitutes an alternative characterization of the tooth form,
relevant for dental studies. However a detailed systematic/
functional analysis, applied to explicit hypotheses, is beyond the
scope of this article and will require a more extensive sample to be
achieved in further studies.
Figure 1. Tridimensional orientation of the molars in the virtual space, example of a Gorilla. A1, alignment of the plane defined by the tipof the dentine horns at protocone (Pro), paracone (Par), metacone (Met) to the x, y plane (P1) of the virtual space; A2, aligned enamel-dentinejunction surface; A3, aligned enamel surface. The lowermost point of each molar cervix is set to (x, y, 0) so that crown height is measured on a z-positive scale. The z axis is positively oriented from the cervix to the occlusal relief of the tooth. B1, the mesial axis (ma), a line joining the tip of thedentine horns at paracone and protocone is set parallel to the x-axis of the virtual space; B2, oriented enamel-dentine junction surface; B3, orientedenamel surface. Not to scale.doi:10.1371/journal.pone.0066142.g001
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Data Acquisition and Analyses
While a wide variety of noninvasive solutions are accessible for
capturing object’s tridimensional forms, microtomographic sys-
tems (m-CT) remain a powerful and efficient tool in retrieving
detailed aspects of dental components morphology (e.g. enamel
occlusal surface, enamel-dentine junction surface) (e.g. [9–
10,12,29,54]). Our molars sample consisting in two gibbons
(Hylobates sp), four gorillas (Gorilla gorilla), three chimpanzees (Pan
troglodytes), five modern humans (Homo sapiens) and six cercopith-
ecoids (two Cercocebus sp., two Cercopithecus sp. and two Papio sp.) and
one South American monkey (Lagothrix sp.). The studied molars
belong to the osteological collections of iPHEP/University of
Poitiers (19th century) which consist exclusively in bone material
(for research and education). None of the molars in our sample
were collected from live animals or humans, besides no animals
were killed specifically for this study. This sample offers an
adequate taxonomic and morphological diversity for appraising
our protocols even though an extended sample size is required for
testing explicit functional/systematical hypotheses. Molars were
scanned using a m-CT VISCOM X8050 (Centre de Microtomo-
graphie at the University of Poitiers).
In order to isolate enamel and dentine materials for each molar,
the virtual volumes reconstructed from microtomographic images
are processed using automatic segmentation tools with manual
correction using �Avizo v7 commercial software. A review of
concepts and practices in 3D image segmentation is beyond the
scope of this notes and the reader may refer to the abundant
literature on this topic [55–58].
Once segmentation is complete, the crown enamel is isolated
from dentine material and pulps canals. The crown enamel
volume data is converted into a polygonal surface (a 3D triangular
mesh) corresponding to a set of tridimensional points (nodes)
connected by edges. This operation allows partitioning the crown
enamel in its inner (enamel dentine junction, EDJ) and outer
(outer enamel surface, OES) components (Figure 1). For analyses
purposes and in order to minimize the computational load for this
note, each EDJ and OES was set to an equivalent reduced amount
of polygons by decimation. The decimation procedure was done
by a re-tessellation of the original polyhedral surface with tooth-
size standardization of the polygonal unit area (i.e., each surface is
constituted by polygons of equivalent area, which area depends of
the tooth size). Following this procedure, all occlusal enamel and
enamel-dentine junction surfaces are constituted by about 22,000
polygons across our sample. Decimation of the original surfaces
does not yield significant alteration of the tooth morphology (see
Figure S1).
Each surface node and surface triangle is precisely referenced by
Cartesian (x, y, z) coordinates in a 3D virtual space. In order to
normalize our result, we choose to orient each molar in their 3D
virtual space using a common reference plane and axis. While the
designation of reference planes for tooth reorientation is an
important step for the following computations, the definition of
such planes may vary according to the aim of the study, the tooth
under consideration, the wear level, the sampled taxa and the
authors (e.g. [59]). Hence, here we choose to align the 3D virtual
surfaces to a geometrically constructed plane without any
preconception on biological or functional meaning, or on
Figure 2. Patch identification for complexity assessment. A, 3D view of a Gorilla second upper molar; B, detail of the paracone showing thesurface polygonal grid; C, orientation of each polygonal element is coded using a chromatic scale, the contiguous triangles with comparableorientation range form a patch. Patch#1, P. #2 and P. #3 are three different patches of polygonal elements. Not to scale.doi:10.1371/journal.pone.0066142.g002
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reproducibility in a future larger, more heterogeneous sample (i.e.,
including more disparate taxa and molar morphologies). The only
prerequisite, for convenience purpose, was to have the occlusal
surface parallel to the viewer plane (e.g. [59–60]). First, each molar
is aligned to a (xy) plane (reference plane) defined by the tip of the
dentine horns at protocone, paracone, metacone (Figure 1A). The
z axis is positively oriented from the cervix to the occlusal relief of
the tooth. Second, each molar is realigned in the reference plane
by having its mesial axis, a line joining the tip of the dentine horns
at protocone and paracone, parallel to the x axis of the 3D virtual
space (Figure 1B). Finally, for convenience purpose, the lowermost
point of each molar cervix is set to (x, y, 0) so that crown height is
measured on a z-positive scale.
Figure 3. Tridimensional morphometric maps and associated chromatic color scales of the principal topographical parameters forOES and EDJ. A, enamel thickness (mm); B, inclination (degree): enamel (B1), enamel-dentine junction (B2); C, orientation (degree): enamel (C1),enamel-dentine junction (C2); D, standardized curvature: enamel (D1), enamel-dentine junction (D2). The figured molars correspond to a subsampleof eight individuals representative of the eight studied genera (from left to right): Homo, Pan, Gorilla, Hylobates, Cercocebus, Papio, Cercopithecus,Lagothrix. In order to improve the readability, the sizes of the molar representations have been modified in A to D; refer to the grey scale molars (firstrow) for relative and absolute size.doi:10.1371/journal.pone.0066142.g003
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Table 1. Measurements and indices for the occlusal surface of enamel and enamel-dentine junction in anthropoid molars.
Id1 d dsd dst C yc Qbi Qp Qmci
Cercocebus #Cb2 0.68 0.17 1.13 0.46 0.42 74 58 1.17 0.32 0.38 0.56 0.89
#Cb4 0.83 0.16 1.31 0.54 0.48 63 72 1.14 0.32 0.37 0.57 1.05
Papio #Pp3 1.22 0.16 2.03 0.28 0.33 80 82 1.16 0.30 0.34 0.54 0.92
#Pp4 1.09 0.18 1.65 0.29 0.25 84 72 1.09 0.30 0.32 0.55 0.87
Cercopithecus #Cc1 0.51 0.12 0.71 0.34 0.25 65 59 1.22 0.30 0.36 0.55 0.89
#Cc2 0.63 0.13 0.95 0.34 0.28 67 58 1.21 0.29 0.35 0.55 0.90
Gorilla #Go1 1.15 0.18 1.58 0.37 0.47 79 53 1.01 0.29 0.29 0.47 0.54
#Go2 1.09 0.23 1.56 0.50 0.76 88 84 0.94 0.30 0.28 0.49 0.58
#Go3 0.92 0.14 1.18 0.64 0.68 74 78 1.01 0.31 0.31 0.54 0.66
#Go4 1.01 0.16 1.29 0.62 0.69 76 68 0.98 0.31 0.31 0.55 0.65
Homo #Ho1 1.44 0.21 2.12 0.66 0.56 60 78 1.02 0.26 0.26 0.41 0.63
#Ho2 1.41 0.22 2.11 0.81 1.17 82 87 0.82 0.35 0.29 0.55 0.63
#Ho3 1.50 0.24 2.42 0.89 0.63 67 60 1.09 0.23 0.24 0.33 0.60
#Ho4 1.48 0.22 2.09 1.12 0.57 60 59 1.12 0.22 0.25 0.34 0.62
#Ho5 1.44 0.31 2.44 0.97 0.72 74 83 1.10 0.29 0.31 0.47 0.66
Pan #Pa1 0.83 0.17 1.30 1.22 1.43 86 82 1.02 0.29 0.30 0.47 0.67
#Pa2 0.82 0.22 1.25 1.11 1.39 127 94 1.04 0.27 0.28 0.45 0.62
#Pa3 0.91 0.16 1.37 1.35 1.54 89 90 0.93 0.32 0.30 0.53 0.76
Hylobates #Hy1 0.54 0.10 0.83 0.90 1.24 47 59 0.98 0.28 0.27 0.40 0.58
#Hy2 0.53 0.12 0.78 1.06 1.35 51 63 1.01 0.27 0.27 0.39 0.57
Lagothrix #Lx1 0.30 0.10 0.42 0.56 0.91 60 64 0.87 0.29 0.25 0.51 0.66
1.Id, specimen number; d/dsd, mean/standard deviation of occlusal enamel thickness; dst standard occlusal minimum enamel thickness; C, occlusal relief index of OES(first column) and EDJ (second column); yc, number of patch for OES (first column) and EDJ (second column); Qbi, blunting index; Qp, relative crest area for OES (firstcolumn) and EDJ; Qmci, maximum convexity index for OES (first column) and EDJ.doi:10.1371/journal.pone.0066142.t001
Figure 4. Enamel thickness variation. A, occlusal enamel thickness (d, whisker diagrams for mean and standard deviation in millimeter); B,enamel thickness distribution (within taxon average, mm) in hominoids (B1) and cercopithecoids/Lagothrix (B2) relative to the corresponding area ofexpression on the molars (mm2).doi:10.1371/journal.pone.0066142.g004
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Having all the molars oriented, morphological and topograph-
ical data have been retrieved from EDJ and OES. The surface
geometry of the molar morphology consists in a matrix of 3D point
coordinates and their connections. Each triangle of the polygonal
surfaces is indexed and can be attached to a variety of signifiers
(e.g. enamel thickness at location, elevation, orientation, and
inclination). Hence, not only individual or average signifier values
are retrievable from precise location on the molar but also their
complete distributions and variations over the whole tooth or a
particular region of interest.
Enamel thickness quantificationThe enamel thickness (d) is computed as the minimum
Euclidean distance corresponding to the distance from each
OES node to the EDJ closest triangle [12–13,24,43,45,61–62], (see
also [28] for additional comments). For analyze purposes, each
OES node index and its triangle counterpart index on EDJ is
stored. The resultant matrix describes a geometrical relationship
between the occlusal surface of the enamel, and the occlusal
surface of the enamel-dentine junction. This OES to EDJ
minimum-distance relationship is used as a basis for comparing
OES and EDJ topographic signifiers in subsequent analyses.
Enamel and dentine topographical signifiersA normalized vectors field has been computed from the 3D
molar triangular mesh and the matrix of normal vector
coordinates at each individual triangle of EDJ and OES has been
recorded. The vector coordinates are used as raw data for
retrieving topographical information of the tooth form, OES and
EDJ being treated independently.
Although numerous descriptors may be generated from OES
and EDJ, we selected here four simple topographical parameters
that have been shown to be of significant interest in dental studies
e.g. in ontogeny, taxonomy or in reconstructing diet habits and
masticatory behaviors.
The variables are calculated from OES and EDJ polygon
coordinates, normalized vector field and d values. All the
computations are fully automated using a program developed
under R [63].
For both OES and EDJ we computed enamel and dentine
elevation (respectively ce and cd), inclination (le/d), orientation
Figure 5. Variations of orientation of enamel occlusal surface. Each profile corresponds to the relative proportion of area expression (inpercentage) of the eight orientation intervals. Since orientation is coded on 360u, the relative contribution of the orientation intervals is given in polarcoordinates. The schematic drawing (lower right) indicates the direction of orientation for the considered surface according to the tooth orientation.Thus, for instance, polygons for which normal vector is in the 90–135u intervals correspond to a mesially oriented surface. Ms1, Ms2, mesial quadrants;Ds1, Ds2, distal quadrants; MB, DB, mesio- and distobuccal quadrants; ML, DL, mesio- and distolingual quadrants.doi:10.1371/journal.pone.0066142.g005
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(ye/d) and curvature (Qe/d). These topographic variables have
been successfully applied, albeit in a different form, to functional,
taxonomic or ontogenetic studies in carnivores, multituberculates,
rodents and primates (e.g. [12,47–48,50]; see also [64–66].
ComputationsThe R program first performs a polygonal indexation then
computes the polygon areas (u), the polygon geometric center
coordinates (i.e., its x, y, z position in the 3D virtual space; x) and
the topographical values (c, l, y). For OES and EDJ, each
polygon is referenced by its constitutive edges and nodes and is
numbered. This step allows for all subsequent computed values to
be precisely associated to its corresponding polygon along with a
precise tridimensional location and an area. The area values are
used as a size proxy (using the number of triangle is unreliable) to
assess the relative occurrence of following topographical variables
(e.g. orientation, inclination).
The orientation, the inclination, and the elevation are computed
for each polygon of OES (ye, le, ce) and EDJ (yd, ld, cd).
The orientation is defined as the direction of the polygon
normal vector in the xy plane of the 3D virtual space and is coded
on 360u. This parameter is equivalent to the one defined in [22,47]
(see also [48]) for topographical analyses of carnivore, primate and
rodent teeth, as a basis for assessing tooth complexity.
The inclination is defined as the angle between the polygon
tangent vector in the -z direction (in the plane perpendicular to xy
and carrying the polygon normal vector) and the horizontal plane
xy. This parameter thus differs from previously defined slope [36] as
‘‘the average change in elevation across the surface’’ ([36] p. 155,
see also [15,48,50,65,67–68]). The inclination (l) is coded on 180u,from 180u for horizontal polygons to 90u for vertical polygons
inclination values below 90u describe re-entrant angles (surfaces).
The elevation is computed as the z coordinate of each polygon
barycenter (xz). This simple parameter allows assessing precisely,
for instance, the height of structures of interest (e.g. cusps, dentine
horns) relative to various planes (e.g. central basin, cervix) or the
relative cuspal heights (e.g. hypocone versus trigonal cusps).
Besides, using polygonal x, y, z coordinates allows precisely
isolating individual cusp morphologies (i.e., individual cusps being
defined by an x, y interval and a z range).
A fourth variable, the mean curvature (Q), has been computed
as the mean value of the two principal curvatures values (i.e., the
minimum and maximum normal curvatures) for each polygon
[69–70]. These quantities measure the deviation from flatness of
the tooth surface (i.e., the occurrence and magnitude of bulging
and hollowing), and are computed for OES and EDJ using
�Avizo v7. In this sense, Q approximates the variable angularity
(i.e., the second derivative of the elevation; [50]) defined by Ungar
and colleagues as the ‘‘change in slope across a surface’’ ([71], p.
3875).
Mean curvatures vary from negative values in strictly concave
regions to positive values in strictly convex regions. Also, the levels
of Q values provide a quantitative assessment of the convexity/
concavity profile; slightly concave or smooth convex regions (e.g.
basin, rounded cusp) have low Q values while highly concave or
sharp convex regions (e.g. groove, dentine horn apex, crest) show
Q values with the highest levels. Regions where a positive and
negative principal curvature cancels each other (i.e., flat regions)
present Q values equal or close to zero.
Second, the R program measures the distribution of orientation
for OES and EDJ polygons and produces subset of polygons
according to a given orientation ranges. For the present study, the
orientation intervals are set to 45u producing eight orientation
groups (e.g. [47–48]). Contiguous polygons within each subset are
identified as a patch (Figure 2) and the complexity (i.e., the number
of these patches within an orientation interval or for the complete
orientation range) is computed [22,47,49,72]. Only patch includ-
ing more than three polygons are considered in this study. For
analyses purposes, each patch is associated to its area value as the
sum of the areas of its polygon parts.
Finally, the program aims to relate OES and EDJ variables in
order to evaluate their correlation. There are no true or sufficient
homologous points on either surface to perform such evaluation,
and polygonal elements cannot be considered as homologous per se.
Geometrical properties of the surfaces can be used as an
alternative for identifying correspondences between OES and
Figure 6. Variation of occlusal enamel and enamel dentine-junction inclination (lv). Values for lv are reported for each specimen, for bothEDJ and OES. lv is computed as the area of expression of polygons with inclination higher than 135u relative to the area of expression of polygonwith inclination lower than 135u. The average lv is given for each taxon.doi:10.1371/journal.pone.0066142.g006
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EDJ polygons. Thus, enamel and dentine polygonal correspon-
dence matrix computed for enamel thickness has been used to
relate OES and EDJ topographical and morphological polygonal
values. The ‘minimum distance’ approach is classically imple-
mented as a 3D surface registrations and comparisons method.
Alternative approach such as ‘minimum normal distance method’
generates equivalent correspondence matrix for our surfaces which
are defined by a high density of points (i.e. [28]).
The R program yields a matrix in which each polygon of OES,
with its morphological and topographical values, is associated to its
corresponding EDJ polygon and respective morphological and
topographical values.
Additional indicesThe computed raw values (c, Q, l, y), were used to calculate a
set of additional indices as an illustration of potential applications
of our 3D method of quantification. Besides, these quantities allow
summarizing the observed variations and facilitating comparisons
with previous studies.
Two measures of enamel thickness are given: (1) the average
occlusal enamel thickness corresponds to the d-mean value for the
occlusal region; (2) the standard occlusal enamel minimum thickness (dst)
as the sum of each polygonal enamel thickness (d) multiplied by its
surface (u), and divided by the EDJ occlusal tridimensional area
(see also [12–13,24,43,61,73]). The marked reliefs such as cusp
tips, crests or grooves tend to be described by more polygons than
planar surfaces in tridimensional models. This effect is minimized
in our sample due to the re-triangulation of the original polyhedral
surfaces. However, the enamel thickness values are weighted by
their associated polygonal area in order to control for the
irregularity of the polygonal mesh.
The relief is an important feature, albeit difficult to characterize,
of the crown form. While the relief is, sensu stricto, merely the
difference in elevation between two sets of points, we define here
relief as the combination of three components which are elevation,
Figure 7. Inclination profiles of anthropoids molars. The profile corresponds, for each taxon (average data), to the EDJ relative proportion ofarea of expression of inclination intervals (increment is 15u).doi:10.1371/journal.pone.0066142.g007
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inclination and area. A marked relief has a maximal elevation for a
minimal base area, the average inclination value is high. It is the
opposite for a slight relief. Thus, in this study (but see [36,50,74–
75] for an alternative computation), the relief is assessed by the
occlusal relief index (C) which is computed in dividing the product of
the area and elevation of polygon which have an inclination higher
than 135u by the area and elevation of polygons which have an
inclination lower than 135u (most of the polygons of the occlusal
surface have inclination comprised in 90–180u).The inclination variation (lv), which represents the distribution
of flat to steep portions of the tooth, is illustrated, for OES and
EDJ occlusal regions, as the distribution of the relative areas
representing particular inclination intervals. In this respect,
inclination range is partitioned in eighteen intervals of 15u each,
and corresponding polygonal area is computed within each
interval.
In the same manner, three dimensional quantification of the
molar occlusal complexity is achieved. The orientation range (y)
being divided in eight intervals of 45u each, the corresponding
polygonal area has been computed within each interval for OES
and EDJ. The orientation variation (yv) is illustrated as the
distribution of the area representing particular orientation
intervals. Besides, the number of patch (yc), and their associate
respective area, is computed for each interval and for the whole
orientation range. (see [47,49,72,75–76] for various applications).
Although C is a meaningful parameter for molar occlusal relief
appraisal, features like grooves, basins and fovea, or ridges and
crests are best described using mean curvature variable (Q). For
instance, Q allows retrieving, for each tooth, the proportion of area
consisting in ‘‘grooves’’ (deep and narrow concavity) and ‘‘crests’’
(sharp or pointing convexity). Only data related to ‘‘crest’’ will be
presented here. In order to control for the size effect when
Figure 8. Standardized mean curvature values of enamel occlusal surface. The position of each taxon on the graph corresponds to the areaproportion of enamel occlusal non-curved surface (left axe, horizontal line is for within taxon average value). The bars illustrate the associateproportion of area of expression of convex (light green)/concave (light orange) to highly convex (green) and extremely concave (red) surfaces(average value, see right panel).doi:10.1371/journal.pone.0066142.g008
Figure 9. Maximum convexity index for enamel and enamel-dentine junction, comparison with occlusal enamel thickness inanthropoids. Each specimen is represented by two circles, one for EDJ (Qmci/EDJ) and one for OES (Qmci/OES). The average occlusal enamel thickness(mm) is given for each taxon (horizontal line). Lx, Lagothrix; Cb, Cercocebus; Cc, Cercopithecus; Pp, Papio; Hy, Hylobates; Go, Gorilla; Pa, Pan; Ho, Homo.doi:10.1371/journal.pone.0066142.g009
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comparing curvature values between diverse anthropoid molars,
curvature is standardized. In this study, we simply adjusted Qvalues by a factor consisting in ratio of (1) the cubic root of the
volume of respectively OES and EDJ of the molar of interest and
(2) the cubic root of the volume of respectively OES and EDJ of a
reference molar. Standardized mean curvature values are used to
compute a maximum convexity index (Qmci) as the sum of the products
of the area of convex polygons by their curvature value, divided by
the OES (or EDJ) tridimensional area. For the occlusal surface,
this index assesses the convexity level (i.e., sharp features with high
Q values are emphasized) along with the convexity expression (i.e.,
its area representation). These two quantities may appear to be
contradictory since sharp features tends to be represented by
smaller surfaces. However, this effect is, at least partially,
compensated by the fact that sharp features (e.g. crests) tend also
to be more elongated than blunt ones.
Although, we did not consider ‘‘crest’’ length in our study, the
maximum convexity index follows Kay [64], and Anthony and Kay
[77] in evaluating the shearing capacity of the molar.
Finally, relationships between OES and EDJ morphological and
topographical values is illustrated using two selected variables: (1)
the relative complexity (yc–e/d) as the ratio of the OES and EDJ
complexity (see e.g. [72]); (2) The blunting index (Qbi) which
measures, for convex features, the degree of which enamel deposit
modifies the enamel-dentine junction morphology, that is, for
instance, how sharp/pointing morphologies of the dentine are
modified in blunt/rounded morphologies by the enamel. The
blunting index is calculated as the ratio of the EDJ crest area and the
EDJ 3D area (Qp/EDJ) divided by the ratio of the OES crest area
and the OES 3D area (Qp/OES).
The morphological and topographical variables have been
computed for each tooth of our sample, and a subsample has been
used to test for correlation between OES and EDJ. For this present
note, our analysis is restricted to the occlusal regions of OES and
EDJ. The OES and EDJ occlusal regions have been defined
discretely as the regions above a plane parallel to the reference
plane and passing respectively by the lowermost point of 1) the
occlusal enamel basin for OES, and 2) the enamel-dentin junction
basin for EDJ. Other aspects of the tooth morphology and
topography, with extension of the ROI to the whole tooth, will be
investigated in further studies.
For visualization purpose, all the computed topographical
values are respectively mapped onto OES and EDJ using
chromatic color scales and presented for the whole tooth.
Results and Discussion
Computed morphological and topographical maps are report-
ed, for a subsample of anthropoid molars (OES and EDJ) on
Figure 3. The topographical variables are reported in Table 1.
The results presented in this section aim to provide an example of
the potential treatments of the data. Formal testing of taxonomic,
developmental or ecological hypotheses is beyond the scope of this
note and will be considered elsewhere using extended sample size.
Figure 10. Relationships between inclination of OES, minimum enamel thickness and inclination of EDJ. Example of Cercocebus (A) andGorilla (B). The correlations and their significance between lOES and d, and between lOES and lEDJ have been computed for about 130 subsamples of1000 inclination and thickness values (resample with replacement on the original data) for each specimen. The correlations are significant for all lOES
and lEDJ comparisons in Cercocebus (A1, red profile) and Gorilla (B1, red profile). The OES inclination is significantly correlated to the enamel thickness(albeit negatively) in Cercocebus (A1, blue profile) while lOES and d present significant positive correlation in 72.1% of the cases in gorillas (B1, blueprofile; significant correlations are marked with a blue diamond). A simplified version of the observed relationship is given for Cercocebus (A2) andGorilla (B2) from a subsample of 250 inclination and thickness values (resample with replacement on the original data). The surfaces of the dots in A2,B2 represent minimum enamel thickness value (scale *10).doi:10.1371/journal.pone.0066142.g010
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Enamel thicknessThe computed enamel thickness values for the occlusal region of
OES (d) are reported on Figures 3A and 4 (mean and standard
deviation are listed in Table 1). Our data are in accordance with
previously reported thicknesses, albeit using different variables (e.g.
AET average enamel thickness [24,43,46,73]; see also AMT average
minimum thickness [61]). Homo presents the greatest average enamel
thickness within hominoids then Gorilla and Pan while highest
values are recorded in Papio within cercopithecoids (Table 1,
Figure 4A). Such hierarchy is maintained using enamel thickness
adjusted for molar size (dst) though lowest Gorilla values being more
similar to those of chimpanzees. The tridimensional quantification
of enamel thickness allows examining its variation over the
occlusal region of the anthropoid molars. The Figure 4B illustrates
the distribution of the occlusal enamel thickness according to its
area of expression within each taxon (see also Figure 3A). The
enamel thickness variance is highest in Homo and closely followed
by Gorilla/Pan then Papio/Cercocebus. The modern Homo sapiens
presents also the highest range of d values (from 0.5 to 2.2 mm on
average) suggesting a more heterogeneous distribution of the
enamel over the enamel-dentine junction in this taxa. Within
modern humans, 42% of the enamel surface corresponds to a dhigher than 1.4 mainly at the protocone (lingual) and at the
hypocone. The gorilla/chimpanzee and the genus Papio present
comparable ranges of d values albeit with different distributions.
The patterns of enamel thickness distribution show notable
disparities between taxa. Within hominoids, Pan presents a
characteristic ‘‘bi-modal’’ shaped curve with comparable repre-
sentation of two enamel thickness classes, 0.6–0.7 mm and 0.8–
1.0 mm. The first class represents thickness at the large central
Figure 11. Measuring the bilophodonty by the mean of polygon orientation distributions. Example of a theoretical case of two cusps(outlined in green) showing various degrees of bilophodonty; a & b illustrate distinct lingual and buccal cusps, c development of buccal and lingualcrests at lingual and buccal cusps, d, loph joining lingual and buccal cusps. The normal vector (red arrow) describing each point of the cusp outline(or polygons for tridimensional data) allows retrieving orientation values along the cusp contour. The cusp contour can be decomposed in differentportions describing same orientation intervals (e.g. 0–45u or 90–135u, only mesial halves of the cusps is shown) numbered from 1 to 8. Thedistribution and the relative contribution of the orientation intervals to the shape of the cusp allow quantifying the development of bilophodonty.Hence for instance, complete bilophodonty is marked from c to d by the deletion of orientation classes 4 and 1 between cusps on their mesial side.doi:10.1371/journal.pone.0066142.g011
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basin while second class corresponds to thickened area around the
crown at the cusp level. The gibbon, the gorilla and the modern
human show unimodal distributions of enamel thickness. Within
cercopithecoids, Papio presents the widest d range (from 0.2 to
1.6 mm). The three cercopithecoid genera show similar patterns of
distribution with thicker enamel at the cusps/lophs level and
thinner enamel at central basin and distal/mesial fovea (indicated
by a step in the d distribution; Figure 4B2).>
OrientationThe variation in orientation (yv) for enamel and enamel-dentine
junction occlusal surfaces is illustrated in Figure 3 (Figure 3C1,
3C2) and Figure 5; complexity (yc) is reported in Table 1.
Considering the respective area of expression of orientation
intervals, yv evidently first depicts overall molar morphology.
Thus, elongated (rectangular) molars tend to have proportionally
higher area of expression for lingual and buccal orientation
intervals than quadrangular molars (Figure 5). However, this
expected pattern is altered by the presence of occlusal features
such as cusps, grooves, crests, and lophs. Both shape and
development of these structures influence the area expression of
orientation intervals. While a rounded cusp tends to add roughly
equivalent area in each interval, features like crests, grooves or
lophs will act only on particular orientation. Hence, yv may
present clear interspecific discrepancies (an analyze of variance of
orientation profiles using shape coordinates show significant
differences between cercopithecoids and hominoids at p,0.05
for OES and at p,0.01 for EDJ), but is expected also to document
subtle variation related to disparate within-taxon expression of
occlusal features.
Theoretically, each orientation interval is expected to represent
12.5% of the total area. The greater deviations from this pattern
are found in cercopithecoids while the hominoids tend to exhibit a
more uniform distribution of the orientation intervals (see the
different types of orientation profiles in Figure 5).
The orientation intervals which present the highest area
proportions correspond, on average, to distal (Ds2) and mesial
(Ms2) quadrants in Cercopithecus and Papio (includes lingual side of
the tooth and lingual portion of the buccal cusps). It is the
distobuccal interval (DB) for all the other genera followed by the
mesial quadrant (Ms2) in Cercocebus, and Homo and Hylobates; by the
distolingual quadrant (DL) in Lagothrix, Gorilla and Pan.
Although the enamel-dentine junction surface (EDJ) does not
present, overall, contrasting information with OES for yv (see
Figure S2), a greater variation is seen for orientation intervals’
representation within and between taxon.
Considering complexity, our results depart from those previously
reported in the literature for anthropoids (Table 1; see e.g. [72]).
The observed dissimilarities can rely on different sample
composition; the complexity presents individual variability and
variation is also expected to occur between species within a same
genus (e.g. within Hylobates, Cercopithecus). Besides, distinct meth-
odologies (e.g. we limit our results to the occlusal portion of the
molar) could also explain the results inconsistencies, and several
aspects are suggested to alter the complexity values. First, it is
worth noticing that our study is based on a 3D triangular
representation of the molar surface while other studies rely on
squared pixels representation of a 2D projection. Such method-
ological distinction is, alone, prone to lead to perceptible variation
in patch count. Besides, the minimum number of contiguous cells/
polygons defining a patch varies according to author (usually from
3 to 6 [47,49,72,75–76]; 3 in this study). This threshold value
directly influences the number of patch, i.e. the complexity, and is
contingent of two inter-related factors that account for resolution:
the cells/polygons size and the tooth size (the number of cells/
polygons). Though procedures of tooth/polygon size normaliza-
tion have been applied in the literature (see e.g. [72]), the
combined effect of the minimum number of cells and the surface
resolution in numbering patch remains unclear (see e.g. Fig-
ure S3). Besides, the integration of particular features like re-
entrant or vertical surfaces in our models may also account for yc
dissimilarities between the present note and other results. Finally,
the tessellation techniques producing the enamel and enamel-
dentine junction surfaces may generate various kinds of noise (i.e.,
incorrect position or orientation of a set of polygons). Although
various techniques exist for noise reduction, the alteration of the
original surface as well as remnant noise may also account for
differences in complexity values between studies.
All the herein aspects are prone to modify yc values between
and within taxa. It suggests, at least, that a detailed examination of
the factors affecting the patch number is needed for assessing the
relevance of complexity in later studies. Indeed, the interpretation of
this quantity turns out to be questionable when one considers the
respective contribution of each orientation interval to the total
value. Thus, substantial variations occur between taxa as expected,
but also within taxa (see Figure S4). The contribution of each
orientation interval to the total complexity notably differs between
individuals with a maximum number of patches being represented
by distinct orientations according to specimens. For instance in
Homo, two individuals shows a greater yc value for the orientation
270–315u, one for 0–45u, one for 180–225u and one for both the
intervals 45–90u and 135–180u. Hence, if one considers that the
total complexity has significance, the way this quantity is acquired is
highly variable. It suggests that the total complexity aggregates
patches with randomly generated orientations over the occlusal
molar surface. In this respect, it seems necessary to reconsider
complexity in taking into account, for instance, the angulation
between contiguous patches. Indeed, a similar complexity (i.e., an
equivalent number of patch) may reflect different morphologies,
contiguous patches yielding sharp edges or smooth transitions may
have different functional meanings.
InclinationThe variation in inclination (lv) for enamel and enamel-dentine
junction occlusal surfaces is illustrated in Figure 3 (Figure 3B1,
3B2) and Figure 6–7. In this study, the inclination is reported as
the variation of the individual polygon values for occlusal OES
and EDJ, measures of average inclination were not considered
here.
Using the relative area of expression of inclination intervals for
describing lv (Figure 6), the enamel-dentine junction surface is
rather flat in Chimpanzee, Hylobates and Lagothrix. Contrarily, the
area corresponding to steep EDJ is relatively more expanded in
cercopithecoids, Gorilla and modern humans. The enamel cap
yield noticeable modification of the EDJ pattern with a relative
flattening of most of the molars (Figure 6). Indeed, the ratio of lv
proportions of EDJ and OES is above 1.0 in Lagothrix (1.34),
Hylobates, Papio (1.15), Gorilla and Pan (1.10). It is close or slightly
below 1.0 in Cercocebus (1.0), Homo (0.94) and Cercopithecus (0.91). Of
course, such result needs to be confirmed using a greater sample; it
also needs to be detailed with a clear distinction of the influence of
dental traits such as crests, grooves and cusps in inclination values.
Further studies will take into account the influence of the amount
of enamel deposition (enamel thickness) in the modification of the
flat/steep relative areas (as presented in paragraph ‘‘covariation’’
here after).
The relative contribution of particular inclination interval to the
tooth surface is illustrated in Figure 7. For simplification and to
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avoid lengthening this technical note, we choose to present results
for EDJ alone, with emphasis on interspecific variation rather than
intraspecific variability (inclination profiles for OES are illustrated
in Figure S5). The cercopithecoids exhibits similar inclination
profiles, distinct from other anthropoids in having higher area
expression for rather steep surfaces (from 105u to 135u).Accordingly, an analyze of variance of inclination profiles using
shape coordinates show significant differences between cercopith-
ecoids and hominoids at p,0.01 for EDJ and p,0.05 for OES. In
Gorilla, the interval 105u–120u is also well represented but this
taxon tends to show more evenly distributed areas in term of
inclination. The modern Homo sapiens profile is comparable to
those of cercopithecoids albeit with a shift towards horizontal
surface, i.e., represented by the 120u–150u inclination intervals.
Besides, the genera Pan, Hylobates and Lagothrix share an important
area expression of the inclination interval 150–165u. However,
while the second greatest area expression corresponds also to
rather horizontal surfaces in Pan (135u–150u), it corresponds to
rather steep surfaces in Hylobates and Lagothrix (105u–120u).
Occlusal relief indexThe computation of the occlusal relief index (C) is listed in Table 1
for OES and EDJ (see also Figure S6). The chimpanzee presents
the highest occlusal relief index, indicating a relatively horizontal (i.e.,
flat), occlusal surface with rather low, smooth reliefs. The
computed C values are on average higher for EDJ than for OES
(although not significantly in our sample; t = 20.44, p = 0.66,
df = 40). It suggests that enamel deposit slightly modifies the EDJ
in accentuating reliefs. Such accentuation is also observed in
Hylobates, Lagothrix, and one Homo specimen, and to Gorilla to a
lesser extent. No significant relationship exists between ‘‘relief
accentuation’’ (i.e., the ratio of COES and CEDJ) and average occlusal
enamel thickness (r = 0.41, p..05; the relationship is significant when
‘‘relief accentuation’’ is compared to a scale-free average occlusal
enamel thickness as the quotient of average occlusal enamel
thickness and occlusal dentine volume [24]; r = 0.59, p,0.01).
However, since the enamel is not evenly deposited over the EDJ,
local variation of the enamel thickness certainly accounts for the
observed differences between CEDJ and COES. The occlusal relief
index is the lowest in cercopithecoids (outside of one Gorilla), with
comparable values for EDJ and OES. This result, indicating
molars with marked relief, is in accordance with the typical
observed morphology in these genera. The modern humans
exhibit notable variation for CEDJ and COES, the C values being
intermediate between those computed in cercopithecoids and
chimpanzees. Also, except for one individual, the occlusal relief index
is lower for EDJ than OES. It suggests, contrary to other
hominoids, that the enamel-dentine junction surface is smoothed
out by the enamel deposit. As noted previously our occlusal relief
index (C) intrinsically differs from classical relief index reported in
the literature (see e.g. [36,42,50,68,74]), but the meanings of these
indices remain unclear. While a significant correlation exists
between C and relief index (i.e., the ratio of the surface area of the
enamel crown, and the surface area of the crown’s projection into
an occlusal plane; r = 20.91 at p,0.01), the two indices vary
conversely (see Figure S6). Although C appears to be more
sensitive to relief irregularity and presents higher variance than
relief index for our sample (see Figure S6), it is clear that similar
index values may arose from different molar morphologies (and
vice versa). It suggests, at least, that improvement of C (and/or relief
index) is needed before use in ecological (e.g. diet) or morphological
studies. For instance, a better appraisal of proportion of negative
versus positive reliefs (e.g. groove versus crests) or a better
distinction between primary (e.g. cusp, loph) versus secondary
reliefs (e.g. cusp crests, crenulations, grooves) is required.
CurvatureThe variation of curvature (Qv) for enamel and enamel-dentine
junction occlusal surfaces is illustrated in Figure 3 (Figure 3D1,
3D2) and curvature indices (Qp, Qbi, Qmci) are reported in Table 1.
The Figure 8 presents the area proportion of standardized
curvature values for OES in our sample (Q values for EDJ are
illustrated in Figure S7). The area proportion of weakly concave/
convex surface (wcs) is high for the selected anthropoid molars and
varies from 54.9% in Cercocebus to 67.1% in Hylobates (Figure 8).
This value is lower in cercopithecoids than in hominoids
(t = 22.26, df = 18 at p,0.05) illustrating a somewhat less
unrelieved ‘‘landscape’’ in monkeys. Besides, salient (convex to
highly convex) reliefs are relatively more extended in cercopith-
ecoids with a greater area for highly convex surfaces, indicator of
the shearing capacity of these molars. Highly convex areas
correspond to the apex of the cusps, to the crests, lophs and to the
mesial and distal marginal ridges. At comparable wcs values, Gorilla
and Pan presents a relatively lower proportion of highly convex
surface than Cercopithecus or Papio (t = 4.96, df = 11 at p,0.01).
Convex surfaces are relatively more extended in the African Apes
while concave to highly concave surfaces are similarly developed.
The relative reduction of highly convex surface is accentuated in
modern humans, a taxon which presents the second highest
relative area for wcs. In Homo, the proportion of convex surface
remains high (22.5%, Figure 8) as well as the area proportion of
highly to extremely concave surfaces (including grooves).
The observed curvature pattern of the selected anthropoid
molars is corroborated by the maximum convexity index (Qmci) and the
blunting index (Qbi, Table 1). Besides, theses indices provide
important hints on curvature modifications of the enamel-dentine
junction by the enamel deposit. The Figure 9 presents the
distribution of Qmci for OES and EDJ in our sample. The maximum
convexity index is, on average, higher in cercopithecoids than in
hominoids (tEDJ = 9.84, df = 16, p,0.01; tOES = 2.77, df = 16,
p,0.05), the latter exhibiting nevertheless substantial individual
variation. Also, the Qmci values for EDJ are consistently higher
than their OES equivalent, suggesting that enamel deposit tends to
blunt the enamel-dentine junction (see also [9]). It is particularly
true for cercopithecoids which present the greater discrepancies
for Qmci between EDJ and OES. Such variation, in accordance
with the results observed for Qbi, does not seem to be related to
molar size or to enamel thickness (Figure 9). Further investigation
is necessary to substantiate our observation and to interpret the
meaning of such a ‘‘blunting’’ effect of the enamel-dentine
junction in cercopithecoids.
CovariationA correlation matrix between nine variables (d, cOES, lOES,
yOES, QOES, cEDJ, lEDJ, yEDJ, QEDJ; significance at p,0.01) has
been computed for each specimen. Our sample presents significant
correlations in most cases with, on average, 78.5% of variable
comparisons being significant per specimen. However, only few
variable comparisons show moderate to strong correlation (from
r = 0.30 to r = 0.73 at p,.01). Highest correlations occur for d/
QOES (e.g. r = 0.69 in Lagothrix; r is about 0.60 in Gorilla) and for c/
l and c/Q comparisons for both OES and EDJ (e.g. r(cEDJ/
lEDJ) = 0.73 in Hylobates; r(cOES/QOES) = 0.48 to 0.50 in Cercopi-
thecus). Considering the relationship between the enamel surface
and the enamel-dentine junction surface, a significant correlation
is repetitively observed for cOES/cEDJ, cOES/QEDJ, and lOES/
lEDJ. For this present note we will focus on the lOES/lEDJ, and
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lOES/d relationships with the example of one Cercocebus specimen
and one Gorilla individual. The Figure 10 presents the correlations,
and their significance, of lOES and d, and of lOES and lEDJ
comparisons. Regarding the amount of data (about 5000 and 7000
value for each variable), we choose to evaluate the correlation
between lOES, lEDJ and d, using about 130 subsamples of 1000
inclination and thickness values (resample with replacement on the
original data) for each specimen. The correlations are significant
for all lOES and lEDJ comparisons in Cercocebus and Gorilla,
suggesting that the enamel-dentine junction inclination primarily
constrains the enamel inclination. Nevertheless, the coefficient of
correlation illustrates a weak to moderate relationship (r varies
from 0.18 to 0.43) with significantly lower correlation in Cercocebus
than in Gorilla. This result indicates that lEDJ cannot account alone
for the observed lOES variation. In this respect, it is reasonable to
consider that variation of enamel thickness may alter the
relationship between lOES and lEDJ. The OES inclination is
significantly and highly correlated to the enamel thickness (albeit
negatively) in Cercocebus (Figure 10A) while lOES and d present
significant positive correlation in only 72.1% of the cases in gorillas
(with weak coefficient of correlation not exceeding 0.19;
Figure 10B). Hence, the enamel does not act similarly in Cercocebus
and Gorilla in modifying the enamel-dentine junction inclination.
Such discrepancy might be explained by different level of enamel
thickness, thicker in Gorilla than in Cercocebus. Also, since the
enamel is not evenly distributed over the occlusal EDJ (e.g. thinner
in the central basin, laterally thicker on cusps), local variations of
the enamel thickness certainly affect the observed relationship
between occlusal lEDJ and lOES. A reanalysis in a more restricted
region of interest (e.g. one cusp), over a larger sample, would yield
to a better understanding of the relationship between lEDJ and
lOES and the role of the enamel thickness in the modification of
lEDJ.
Conclusions and Prospects
Our approach is shown to be a useful tool for characterizing
tooth form and is expected to provide developments in several
fields of dental studies. The topographic parameters originally
described by [50] are quantified in three dimensions without
concealing the information carried by reentrant angles or vertical
walls (e.g. [48,65]). Such information could be suitable in studying
particular aspects of the tooth morphology. For instance, small
insectivorous mammals classically have sharp cusps, of which they
use the entire surface to penetrate the cuticle of arthropods. But
these cusps are often slightly curved, which hides areas and
corresponding data (e.g. the orientation patch number) located in
the constituted reentrants during a 2D complexity analysis.
Similarly, muroid rodents have distributions of inclination values
that are assumed to vary considerably according to their occlusal
grades [48]. Among them, rodents with extreme tooth morphology
such as the Arvicolinae, for instance, display very important
reentrants, because of the inclination of the pillars of their
hypsodont molars, which may bias the comparison with brachy-
odont muroids.
Also, though several studies have recently undertaken three-
dimensional analyses of the tooth structural morphology (e.g. [9–
11,78]), the covaration between enamel and enamel-dentine
junction is for the first time, to our knowledge, considered in a
quantitative way using their geometric relationship. Besides, the
proposed method enables an accurate localization of every features
of the occlusal morphology thanks to the collected 3D data. The
integration of topographic parameters along with their precise
localization provides a new opportunity to study the variation of
these parameters (i.e. their distribution) on the whole surface of the
tooth, or for more reduced regions of interest (e.g. the occlusal
surface in this work, but applies also to particular features like
cusps). The size component of these distributions, i.e. their surface
extension, completes their study. Targeting the modifications
through localization is also an opportunity to define precisely
dental cusps and crests, of which definition is sometimes difficult in
some species of mammals, especially when it comes to evaluating
the intraspecific variation of a taxon or the evolution of a
morphotype within an evolutionary lineage. Established parame-
ters can thus be used to determine thresholds for which tooth
elements can be considered as cusps or accessory cusps, gutters or
crests.
The approach proposed in the present paper raises several
important questions that were not specifically addressed in
previous studies but may be discussed through examples selected
in our dataset: 1) the taxonomical and functional signal carried out
by the topographical descriptors; 2) the relationship between
dental complexity and diet; 3) the influence of the enamel layer on
topographic parameters including curvature.
First, the selected topographic parameters (e.g. orientation,
inclination) enable to distinguish high-ranking (family level) and
low-ranking (genus level) taxa among anthropoids as evaluated
here using unworn to slightly worn molars. This result is expected
since topographic parameters obviously describe morphological
aspect of the tooth. Thus, bilophodont molars in cercopithecoids
exhibit orientation and inclination values in accordance with the
development of transverse lophs between cusps contrary to
bunodont molars in hominoids. Besides, curvature seems to be a
relevant parameter for accounting subtle differences within
cercopithecoids and hominoids allowing describing morphological
features potentially associated to the tooth function, like sharpness
versus bluntness [79–80]. Thus, the distinctions emphasized in the
present work can complement results from geometric morpho-
metrics in which occlusal cusp pattern or even crown outline are
described (e.g. [19,33]). Our preliminary results highlight the
potential of topography as a taxonomical tool which will have to
be assessed on variously worn specimens considering that extreme
tooth wear may question such a potential (but one can reach the
same conclusion whatever the method of investigation used for
interpreting morphology in term of taxonomy). Besides, our
approach may also enable to quantify the emergence and the
retention of diagnostic dental features such as bilophodonty in Old
World monkeys (to decipher the respective part of the OES and
EDJ in the development of that feature; Figure 11). In this way the
evolution of primates is characterized by the recurrent emergence
of the hypocone in their different lineages as in Adapidae [81],
likely according to distinct evolutionary pathways. The variables
featured in this work as well as the localization data should
contribute to the study of the various modes of emergence of this
key character.
Moreover the spatialized approach developed in this work offers
the opportunity to practically assess the ‘local’ influence of some
topographic parameters initially calculated for the entire crown, as
inclination [48] and complexity (e.g. [22]). More generally,
targeting the modifications through localization is a way to
appraise, on the occlusal surface, the topographical variations of
each element in respect to the functional constraints induced by
diet (e.g. [47]) and occlusion [48,65]. For instance, the measure-
ment of shearing crest development on primate molars is regularly
used to infer the diet of fossil species (e.g. [64,78,82]). However,
while various types of crest reliefs are present on the occlusal
surface of the tooth, their location, height, length, orientation, and
sharpness may have different functional meanings depending of
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the body size, dietary habits, and masticatory phases of the taxa
under consideration. The 3D localization and distribution of the
parameters presented in this work is expected to allow accounting
for these patterns of variation when studying particular structures
such as dental crests. Similar work could be undertaken to evaluate
the functional significance, if any, of the grooves of the occlusal
surface.
Second, analyzing the dental topography in its comprehensive
tridimensional aspect yields unanticipated results somewhat
contrasting with previous studies. For instance, methodological
issues may explain the variations observed between our results
about topographic complexity and those of the literature (e.g.
[72]), but also suggests that previous analyzes did not take into
account of the entire tooth complexity. The complexity index
defined by [22] illustrates the relationships between the number of
patches observed on the occlusal surface and diet, the patches
being supposed to reflect the tooth breakage sites. Carnivorous
species have a reduced number of patches, while in herbivorous
species this number is high. The relationship between complexity
and diet seems to be more difficult to interpret in primates (see also
[72]): despite our sample did not include purely insectivorous
primates like Tarsius, the complexity variable should have
highlighted differences between omnivorous taxa incorporating
insects in their diet (e.g. Pan, Cercocebus), and more exclusively
frugivorous taxa (e.g. Cercopithecus, Hylobates), which was not the
case. In this respect, a sample encompassing more taxa, i.e. having
a greater variation in dietary habits, would be more suitable to
assess relationships between complexity and diet in this group. If a
link between topographic complexity and all diets should be
confirmed by 3D analyses, localization should determine whether
the adaptive signal is carried exclusively by the total number of
patches, or is the byproduct of each orientation class’ contributions
to the total complexity. Our study suggests that similar values of
complexity can be obtained by different relative contribution of
orientation ranges in individuals of the same species. Hence
equivalent complexity may arise from different occlusal patterns
and therefore may have different functional outcomes in the
context of similar masticatory movements. On the long range, the
reappraisal of similar/different morphologies for comparable diet
in tridimensional and integrative (morphology, topography, size)
way is necessary.
Finally, the localization of the enamel topographic parameters
and their matching with the dentine topographic parameters,
associated with localized quantifications of the enamel thickness, is
prone to improve our understanding of the respective influences of
the enamel-dentine junction and the enamel layer over crown
morphology. In the early stages of tooth development, the enamel-
dentine junction undergoes folding controlled by cellular signaling
centers known as the secondary enamel knots, ultimately
responsible for cusp patterning (e.g. [83]). This folding takes place
prior to the differentiation of the enamel-forming ameloblasts from
the inner enamel epithelium and thus before the secretion of the
enamel layer, which partially modifies the morphological signal
carried by the enamel-dentine junction. The morphology of the
enamel-dentine junction and the thickness variations of the enamel
layer appear to be controlled by distinct genes (e.g. [84–85]). Our
preliminary results indicate that as expected the dentine enamel
junction carries most of the occlusal morphology, however the
enamel layer influences at least the blunting of the curvature of the
dental topography, which may be associated with dietary
specializations. Further studies on fossil lineages could potentially
reveal that convergent emergences of similar occlusal topographies
occurred following differential responses (or different selective
mechanisms) of the enamel-dentine junction and enamel layer.
Hence, the degree of independency of OES and EDJ morphol-
ogies is supposed to reflect the way the tooth morphotype is
selected. In evo-devo analyses, our methods could not only help to
determine whether changes implied by mutant genes influence the
enamel dentine junction, the enamel layer or both (for example,
variations of cusp slopes have been observed in knockout mice, e.g.
[85], and have to be characterized), but could also bring localized
quantifications of these changes, to quantify the rate of morpho-
logical change depending on the gene expression. On a theoretical
level, it will be possible to perform covariation analyses to test
whether there is an influence of the morphology of the enamel-
dentine junction on the secretion of the enamel band and vice versa.
Our approach demonstrates to be a useful tool for character-
izing and comparing tooth form and is therefore recommended as
a component – possibly coupled with other methods such as
geometric morphometrics or Occlusal Fingerprint Analysis (see
e.g. [35,39]) – in further dental studies. Besides, the developed
analytical tools and procedures are suggested to apply to other
tissues requiring a detailed tridimensional characterization.
Supporting Information
Figure S1 Surface alteration between original anddecimated OES in two representative molars of Homo(A) and Pan (B). The figure presents the alteration of the
decimated surface as the distribution of the minimum distances
from original to decimated polygon mesh. Maximum values (in
millimeter) are +0.09 and 20.10 in Homo 5 (average +0.0036/
20.0039), and +0.083 and 20.055 for Pan 1 (average +0.058/
20.0057). Color scales indicate negative and positive distances
from original to decimated surface (in millimeter). Although the
reduction of polygon number may mask small morphological
features, it prevents from documenting uninformative variation
related to irregularity in individual polygon position and
orientation. The decimation procedure does not change the
overall shape of the tooth under consideration. The decimated
surfaces correspond on average to 99% or the original area (e.g.
99.18% for Homo 5 and 99.08% for Pan 1). The decimation
procedure typically affects the expression of crests and grooves
(e.g. depth/elevation, see the case of chimpanzee and its highly
crenulated occlusal enamel surface). However, the magnitude of
morphological change remains low. While a lessened decimation
procedure has to be considered for detailed studies of OES and
EDJ, the present mesh resolution remains suitable for this note
with reduced unwarranted noise and computational loads.
(TIF)
Figure S2 Relative area of expression (mm2) of orien-
tation intervals (increment is 456) for enamel-dentine
junction (EDJ) and enamel occlusal surfaces (OES). A,
Lagothrix; B, Cercocebus; C, Cercopithecus; D, Papio; E, Hylobates; F,
Gorilla; G, Pan; H, Homo.
(TIF)
Figure S3 Relationships between number of patches(complexity, yc) and 3D occlusal area. A, OES, the star and
the associated illustrated molar correspond to one chimpanzee
specimen (P#2) showing a particularly high number of patch; B,
OES, the specimen P#2 has been removed from the analysis; the
star and the associated illustrated molar correspond to the second
highest number of patch in chimpanzee. C, EDJ, note the
variation in gorilla. For A, B, C, molar occlusal complexity (yc) is
in abscissa and molar 3D occlusal area (mm2) in ordinate. D, OES:
relationship between complexity computed on decimated surface
(yc/d this study, abscissa) and complexity computed on the full
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PLOS ONE | www.plosone.org 15 June 2013 | Volume 8 | Issue 6 | e66142
resolution surface (yc, ordinate). Note that higher resolution (i.e.,
increasing the number of polygon describing each occlusal surface)
yields higher complexity values. E. EDJ: relationship between yc/d
(this study, abscissa) and yc (ordinate).
(TIF)
Figure S4 Relative contribution of the partial number ofpatches at each orientation interval to the total com-plexity. The complete orientation range is divided in eight
orientation intervals of 45u each, each color representing one
particular orientation interval. Each ring corresponds to one
specimen. The white dot indicates the highest computed (partial)
complexity for a distribution. A, Cercocebus; B, Cercopithecus; C,
Papio; D, Lagothrix; E, Hylobates; F1-F2, Gorilla; G1-G2, Pan; H1-H3,
Homo.
(TIF)
Figure S5 Inclination profiles of anthropoid molars.The profile corresponds, for each taxon (average data), to the OES
relative proportion of area of expression of inclination intervals
(increment is 15u). Note how enamel deposit modifies the
inclination profiles of EDJ (Figure 8).
(TIF)
Figure S6 Occlusal relief index in anthropoids. A,
relationship between OES and EDJ occlusal relief index (C). B,
comparison between occlusal relief index for OES (COES) and relief
index (RI, sensu Dennis et al., 2004; M’Kirera and Ungar, 2003,
Ungar and Williamson 2000). Note the flattening of the RI profile
compared to COES. Dennis JC, Ungar, PS, Teaford M. F.,
Glander K. E. 2004. Dental Topography and Molar Wear in
Alouatta palliate From Costa Rica. American Journal of Physical
Anthropology 125: 152–161. M’Kirera F., Ungar P. 2003.
Occlusal Relief Changes With Molar Wear in Pan troglodytes
troglodytes and Gorilla gorilla gorilla. American Journal of Primatology 60:
31–41. Ungar P., Williamson M. 2000. Exploring the effects of
toothwear on functional morphology: a preliminary study using
dental topographic analysis. Palaeontologia Electronica, vol. 3: 1–
18.
(TIF)
Figure S7 Standardized mean curvature value of enam-el-dentine junction surface. The position of each taxon on the
graph corresponds to the area proportion of enamel occlusal non-
curved surface (left axe, horizontal line is for within taxon average
value). The bars illustrate the associate proportion of area of
expression of convex (light green)/concave (light orange) to
highly/extremely convex (green) and highly concave (orange)
surfaces (average value, see right panel).
(TIF)
Acknowledgments
We wish to thank all the members of iPHEP (UMR 7262-Universite de
Poitiers; CNRS: INEE Institut Ecologie et Environnement), particularly G.
Merceron and A. Pinton for helpful comments, G. Florent and C. Noel for
administrative guidance, X. Valentin for technical support. We greatly
thank two anonymous reviewers and the academic editor Luca Bondioli for
their thorough review of our work; their valuable comments greatly help to
improve our manuscript.
Author Contributions
Conceived and designed the experiments: F. Guy VL. Performed the
experiments: F. Guy F. Gouvard. Analyzed the data: F. Guy F. Gouvard
VL . Contributed reagents/materials/analysis tools: F. Guy F. Gouvard
AE RB VL. Wrote the paper: F. Guy VL. Developed the 3D method for
topographical quantification and implements the R programs: F. Guy.
Defined the microtomography acquisition settings: RB F. Guy. Acquired
the scan data: F. Guy RB VL. Reconstructed the 3D data and acquired the
surface data: AE F. Guy F. Gouvard.
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